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Advisor(s)
Abstract(s)
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that the solutions of the fractional problems coincide with the solutions of the corresponding non-fractional variational problems when the order of the discrete derivatives is an integer value.
Description
Keywords
Calculus of variations Euler-Lagrange equation Fractional difference calculus Fractional summation by parts Legendre necessary condition
Citation
Publisher
American Institute of Mathematical Sciences (AIMS)